Learning to rank has become an important part in the fields of machine learning and statistical learning. Rankings are indeed present in many applications, including cognitive psychology, recommender systems, sports tournament or automated algorithm choices. Rankings are however prone to subjectivity (when provided by users) and to incompleteness (when a contestant is missing, or users only report partial preferences). Robust or cautious approaches may overcome such issues. In this paper, we develop a Bayesian robust approach for a commonly used parametric model, the Plackett-Luce (PL) model. This allows us to obtain interval-valued parameter estimates for the strength parameter of the Plackett-Luce model. We illustrate our method with both synthetic and real data to show the usefulness of skeptic inference.